Anomalous structure and dynamics of the Gaussian-core fluid

It is known that there are thermodynamic states for which the Gaussian-core fluid displays anomalous properties such as expansion upon isobaric cooling (density anomaly) and increased single-particle mobility upon isothermal compression (self-diffusivity anomaly). Here, we investigate how temperature and density affect its short-range translational structural order, as characterized by the two-body excess entropy. We find that there is a wide range of conditions for which the short-range translational order of the Gaussian-core fluid decreases upon isothermal compression (structural order anomaly). As we show, the origin of the structural anomaly is qualitatively similar to that of other anomalous fluids (e.g., water or colloids with short-range attractions) and is connected to how compression affects static correlations at different length scales. Interestingly, we find that the self-diffusivity of the Gaussian-core fluid obeys a scaling relationship with the two-body excess entropy that is very similar to the one observed for a variety of simple liquids. One consequence of this relationship is that the state points for which structural, self-diffusivity, and density anomalies of the Gaussian-core fluid occur appear as cascading regions on the temperature-density plane; a phenomenon observed earlier for models of waterlike fluids. There are, however, key differences between the anomalies of Gaussian-core and waterlike fluids, and we discuss how those can be qualitatively understood by considering the respective interparticle potentials of these models. Finally, we note that the self-diffusivity of the Gaussian-core fluid obeys different scaling laws depending on whether the two-body or total excess entropy is considered. This finding, which deserves more comprehensive future study, appears to underscore the significance of higher-body correlations for the behavior of fluids with bounded interactions.

Figure 1

(Color online) (a) Self-diffusivity $D$ and (b) structural order metric $-s_2$ versus density $\rho$ at temperatures $T=0.01$, 0.013, 0.018, 0.025, 0.035, 0.05, 0.07, 0.1, 0.15, 0.2, 0.3, 0.4, 0.5, 0.7, 1.0, 1.2, and 1.5 for the GC fluid. Arrows indicate increasing temperature. Solid green (gray) lines in (a) and (b) correspond to minima in $D$ and maximum in $-s_2$, respectively. (c) Rosenfeld scaled diffusivity versus $-s_2$ at all densities and temperatures studied. The solid line represents the empirical Rosenfeld scaling law $0.58\text{exp}\left(0.78s_2\right)$ and the dashed curve represents the low-density behavior expected for soft spheres $0.37{\left(-s_2\right)}^{-2/3}$. (Lower right panel) Pair correlation function $g\left(r\right)$ and cumulative order integral $I_{s_2}\left(r\right)$ along the isotherm $T=0.025$ [red curve in (b)] for two density ranges [(d) and (e)] $\rho \le 0.2$ [below the maximum in $-s_2\left(\rho \right)$] and [(f) and (g)] $\rho \ge 0.2$ [above the maximum in $-s_2\left(\rho \right)$]. In (d)–(g), arrows indicate increasing $\rho$.

Figure 2

(Color online) (a) Boundaries of the structural, diffusivity, and density anomalies in the temperature-density plane, as calculated from simulation data. The inset shows the boundary of the region of density anomalies on an expanded scale. The symbols are the locations of the extrema and arrows are in the direction of the anomalous regions. (b) Schematic representation of anomalous regions.

Figure 3

(Color online) (a) Rosenfeld scaled diffusivity versus excess entropy $-s^{\text{ex}}$. The solid and dashed curves, as well as the symbols, are the same as those in Fig. 1c. The arrow is in the direction of increasing density. (b) Temperature scaled diffusivity $D{T}^{-1/2}$ versus $-s^{\text{ex}}$. The data represent all densities and temperatures considered in this study.